if you fully charge the battery and you say it starts right up,
it should be able to start and run for a few times and miles without needing charged again
i suspect a draw on the battery
it's been a while since i worked on a generator
i'd start by polarizing the generator again
you should know how to polarize a generator since you own one
if not
http://starautoelectric.com/instruct...ing-generator/
if that doesn't work, time to pull it apart and check the brushes, easy peasy
then you move on to the regulator, but check those first
doesn't hurt to check out and maybe continuity check a few wires